Problem: Simplify the following expression: $k = \dfrac{30r^2 + 10r}{10r^2 + 20qr} + \dfrac{20r^2 - 30qr}{10r^2 + 20qr}$ You can assume $p,q,r \neq 0$.
Explanation: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{30r^2 + 10r + 20r^2 - 30qr}{10r^2 + 20qr}$ $k = \dfrac{50r^2 + 10r - 30qr}{10r^2 + 20qr}$ The numerator and denominator have a common factor of $10r$, so we can simplify $k = \dfrac{5r + 1 - 3q}{r + 2q}$